Q. 3 F5.0( 2 Votes )

Prove the following identities.

(1 + cotθ – cosec θ)(1 + tanθ + secθ) = 2

Answer :

Consider LHS,


LHS = (1 + cotθ – cosecθ) (1 + tanθ + secθ)


Expanding the above,


(1 + cotθ – cosecθ) (1 + tanθ + secθ)


= 1 + tanθ + secθ + cotθ + cotθtanθ + cotθsecθ – cosecθ –cosecθtanθ –cosecθsecθ


We know that = secθ, = cosecθ, = tanθ and = cotθ.


= 1 + tanθ + secθ + cotθ + 1 + cosecθ – cosecθ – secθ – cosecθsecθ


We know that tanθ + cotθ = cosecθsecθ.


= 1 + cosecθsecθ – cosecθsecθ + 1


(1 + cotθ – cosecθ) (1 + tanθ + secθ) = 2 = RHS


Hence proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Trigger on TrigonometryChamp Quiz | Trigger on TrigonometryChamp Quiz | Trigger on Trigonometry47 mins
Basics of TrigonometryBasics of TrigonometryBasics of TrigonometryFREE Class
NCERT | Trigonometric IdentitiesNCERT | Trigonometric IdentitiesNCERT | Trigonometric Identities52 mins
Champ Quiz | Trigonometry Important QuestionsChamp Quiz | Trigonometry Important QuestionsChamp Quiz | Trigonometry Important Questions33 mins
Solving NCERT Questions on Trigonometric IdentitiesSolving NCERT Questions on Trigonometric IdentitiesSolving NCERT Questions on Trigonometric Identities56 mins
NCERT | Imp. Qs. on TrigonometryNCERT | Imp. Qs. on TrigonometryNCERT | Imp. Qs. on Trigonometry42 mins
Quiz | Trail of Mixed Questions on TrigonometryQuiz | Trail of Mixed Questions on TrigonometryQuiz | Trail of Mixed Questions on Trigonometry59 mins
Champ Quiz | NTSE TrigonometryChamp Quiz | NTSE TrigonometryChamp Quiz | NTSE Trigonometry50 mins
Testing the T- Ratios of Specified AnglesTesting the T- Ratios of Specified AnglesTesting the T- Ratios of Specified Angles57 mins
Foundation | Cracking Previous Year IMO QuestionsFoundation | Cracking Previous Year IMO QuestionsFoundation | Cracking Previous Year IMO QuestionsFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses